%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL024-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sNshUBGK5I true
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:35:02 PM UTC 2026
% Result : Unsatisfiable 150.70s 25.71s
% Output : Refutation 150.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sNshUBGK5I true
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 16:20:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Running portfolio for 300 s
% 0.10/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Number of cores: 8
% 0.10/0.37 % Python version: Python 3.12.3
% 0.10/0.38 % Running in FO mode
% 0.44/0.67 % Total configuration time : 435
% 0.44/0.67 % Estimated wc time : 1092
% 0.44/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.48/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 150.70/25.71 % Solved by fo/fo13.sh.
% 150.70/25.71 % done 4926 iterations in 24.861s
% 150.70/25.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 150.70/25.71 % SZS output start Refutation
% 150.70/25.71 thf(a_type, type, a: $i).
% 150.70/25.71 thf(is_a_theorem_type, type, is_a_theorem: $i > $o).
% 150.70/25.71 thf(equivalent_type, type, equivalent: $i > $i > $i).
% 150.70/25.71 thf(c_type, type, c: $i).
% 150.70/25.71 thf(b_type, type, b: $i).
% 150.70/25.71 thf(xgk, axiom,
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 ( equivalent @
% 150.70/25.71 X @
% 150.70/25.71 ( equivalent @
% 150.70/25.71 ( equivalent @ Y @ ( equivalent @ Z @ X ) ) @ ( equivalent @ Z @ Y ) ) ))).
% 150.70/25.71 thf(zip_derived_cl1, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @ X0 @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ (equivalent @ X2 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X1))))),
% 150.70/25.71 inference('cnf', [status(esa)], [xgk])).
% 150.70/25.71 thf(zip_derived_cl1, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @ X0 @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ (equivalent @ X2 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X1))))),
% 150.70/25.71 inference('cnf', [status(esa)], [xgk])).
% 150.70/25.71 thf(zip_derived_cl1, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @ X0 @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ (equivalent @ X2 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X1))))),
% 150.70/25.71 inference('cnf', [status(esa)], [xgk])).
% 150.70/25.71 thf(condensed_detachment, axiom,
% 150.70/25.71 (( ~( is_a_theorem @ ( equivalent @ X @ Y ) ) ) |
% 150.70/25.71 ( ~( is_a_theorem @ X ) ) | ( is_a_theorem @ Y ))).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl4, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl5, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl7, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl23, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X3)) @
% 150.70/25.71 X3))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl51, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl23, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X3)) @
% 150.70/25.71 X3))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl513, plain,
% 150.70/25.71 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl23])).
% 150.70/25.71 thf(zip_derived_cl7, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl527, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X0 @ X1)) @ X1))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl51, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl4, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl5, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl8, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ X1 @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl9, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ X1)
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X2 @ (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl13, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X1)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X2)
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl9, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl18, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | ~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ X1))),
% 150.70/25.71 inference('simplify', [status(thm)], [zip_derived_cl13])).
% 150.70/25.71 thf(zip_derived_cl27, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | ~ (is_a_theorem @ X1)
% 150.70/25.71 | ~ (is_a_theorem @ X0))),
% 150.70/25.71 inference('condensation', [status(thm)], [zip_derived_cl18])).
% 150.70/25.71 thf(zip_derived_cl7, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl29, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ X1)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl512, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 ( (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X2 @ X1)))
% 150.70/25.71 | ~ (is_a_theorem @ X2))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl29])).
% 150.70/25.71 thf(zip_derived_cl23863, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X0)))
% 150.70/25.71 | ~ (is_a_theorem @ X1))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl512])).
% 150.70/25.71 thf(zip_derived_cl23, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X3)) @
% 150.70/25.71 X3))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl8, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ X1 @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl5, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl11, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl53, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X4)
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ X4 @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl11])).
% 150.70/25.71 thf(zip_derived_cl0, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.71 thf(zip_derived_cl631, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @ X4)
% 150.70/25.71 | ~ (is_a_theorem @ X4)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl672, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 150.70/25.71 ( (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | ~ (is_a_theorem @ X4)
% 150.70/25.71 | ~ (is_a_theorem @ X0))),
% 150.70/25.71 inference('simplify', [status(thm)], [zip_derived_cl631])).
% 150.70/25.71 thf(zip_derived_cl31994, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 ( (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | ~ (is_a_theorem @ X0))),
% 150.70/25.71 inference('condensation', [status(thm)], [zip_derived_cl672])).
% 150.70/25.71 thf(zip_derived_cl513, plain,
% 150.70/25.71 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl23])).
% 150.70/25.71 thf(zip_derived_cl5, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl542, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl51, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl7, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl511, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 ( (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @
% 150.70/25.71 (equivalent @ X2 @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X2 @ X1)))))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl4470, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X1) @ X0))
% 150.70/25.71 | (is_a_theorem @ X1))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl542, zip_derived_cl511])).
% 150.70/25.71 thf(zip_derived_cl51, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)))
% 150.70/25.71 | (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl4, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl516, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X0 @ X0)))
% 150.70/25.71 | ~ (is_a_theorem @ X1))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl4])).
% 150.70/25.71 thf(zip_derived_cl4579, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ X1)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X0 @ X0) @ X1)))),
% 150.70/25.71 inference('s_sup+', [status(thm)],
% 150.70/25.71 [zip_derived_cl4470, zip_derived_cl516])).
% 150.70/25.71 thf(zip_derived_cl542, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ (equivalent @ X1 @ X0))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl4722, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X1) @ X0))
% 150.70/25.71 | ~ (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup+', [status(thm)],
% 150.70/25.71 [zip_derived_cl4579, zip_derived_cl542])).
% 150.70/25.71 thf(zip_derived_cl511, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 ( (is_a_theorem @ X0)
% 150.70/25.71 | ~ (is_a_theorem @
% 150.70/25.71 (equivalent @ X2 @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ X0) @ (equivalent @ X2 @ X1)))))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl5483, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ X2) @
% 150.70/25.71 (equivalent @ (equivalent @ X1 @ X1) @ X0)))
% 150.70/25.71 | (is_a_theorem @ X2))),
% 150.70/25.71 inference('s_sup-', [status(thm)],
% 150.70/25.71 [zip_derived_cl4722, zip_derived_cl511])).
% 150.70/25.71 thf(zip_derived_cl36843, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @
% 150.70/25.71 (equivalent @ X2 @ (equivalent @ X1 @ (equivalent @ X0 @ X0))))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)],
% 150.70/25.71 [zip_derived_cl31994, zip_derived_cl5483])).
% 150.70/25.71 thf(zip_derived_cl527, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X0 @ X1)) @ X1))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl5, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | ~ (is_a_theorem @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))
% 150.70/25.71 | (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 150.70/25.71 thf(zip_derived_cl1257, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X0)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ X1 @
% 150.70/25.71 (equivalent @ X2 @ (equivalent @ X2 @ (equivalent @ X1 @ X0))))))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl40619, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i]:
% 150.70/25.71 ( (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X0) @ X1))
% 150.70/25.71 | ~ (is_a_theorem @ X0))),
% 150.70/25.71 inference('s_sup+', [status(thm)],
% 150.70/25.71 [zip_derived_cl36843, zip_derived_cl1257])).
% 150.70/25.71 thf(zip_derived_cl23, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)) @
% 150.70/25.71 (equivalent @ X2 @ X3)) @
% 150.70/25.71 X3))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl7, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl5])).
% 150.70/25.71 thf(zip_derived_cl52, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 150.70/25.71 (is_a_theorem @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ X0 @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @
% 150.70/25.71 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.71 (equivalent @ X3 @ X2)) @
% 150.70/25.71 (equivalent @ X1 @ X0)) @
% 150.70/25.71 X4)) @
% 150.70/25.71 X4))),
% 150.70/25.71 inference('s_sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl7])).
% 150.70/25.71 thf(zip_derived_cl513, plain,
% 150.70/25.71 (![X0 : $i]: (is_a_theorem @ (equivalent @ X0 @ X0))),
% 150.70/25.71 inference('s_sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl23])).
% 150.70/25.71 thf(zip_derived_cl4, plain,
% 150.70/25.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.71 (~ (is_a_theorem @ X2)
% 150.70/25.71 | (is_a_theorem @
% 150.70/25.71 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.72 (equivalent @ X1 @ X0))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 150.70/25.72 thf(zip_derived_cl1, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (is_a_theorem @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @ (equivalent @ X1 @ (equivalent @ X2 @ X0)) @
% 150.70/25.72 (equivalent @ X2 @ X1))))),
% 150.70/25.72 inference('cnf', [status(esa)], [xgk])).
% 150.70/25.72 thf(zip_derived_cl8, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X2)
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | (is_a_theorem @
% 150.70/25.72 (equivalent @ X1 @ (equivalent @ X0 @ (equivalent @ X1 @ X2)))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl5])).
% 150.70/25.72 thf(zip_derived_cl4, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X2)
% 150.70/25.72 | (is_a_theorem @
% 150.70/25.72 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @
% 150.70/25.72 (equivalent @ X1 @ X0))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl0])).
% 150.70/25.72 thf(zip_derived_cl29, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @ X1)
% 150.70/25.72 | (is_a_theorem @
% 150.70/25.72 (equivalent @ (equivalent @ X0 @ (equivalent @ X1 @ X2)) @ X2)))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl27, zip_derived_cl7])).
% 150.70/25.72 thf(prove_pyo, conjecture,
% 150.70/25.72 (is_a_theorem @
% 150.70/25.72 ( equivalent @
% 150.70/25.72 ( equivalent @ ( equivalent @ a @ ( equivalent @ b @ c ) ) @ c ) @
% 150.70/25.72 ( equivalent @ b @ a ) ))).
% 150.70/25.72 thf(zf_stmt_0, negated_conjecture,
% 150.70/25.72 (~( is_a_theorem @
% 150.70/25.72 ( equivalent @
% 150.70/25.72 ( equivalent @ ( equivalent @ a @ ( equivalent @ b @ c ) ) @ c ) @
% 150.70/25.72 ( equivalent @ b @ a ) ) )),
% 150.70/25.72 inference('cnf.neg', [status(esa)], [prove_pyo])).
% 150.70/25.72 thf(zip_derived_cl2, plain,
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)))),
% 150.70/25.72 inference('cnf', [status(esa)], [zf_stmt_0])).
% 150.70/25.72 thf(zip_derived_cl0, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ (equivalent @ X0 @ X1))
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | (is_a_theorem @ X1))),
% 150.70/25.72 inference('cnf', [status(esa)], [condensed_detachment])).
% 150.70/25.72 thf(zip_derived_cl3, plain,
% 150.70/25.72 (![X0 : $i]:
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a))))
% 150.70/25.72 | ~ (is_a_theorem @ X0))),
% 150.70/25.72 inference('s_sup+', [status(thm)], [zip_derived_cl2, zip_derived_cl0])).
% 150.70/25.72 thf(zip_derived_cl104, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @ X1)
% 150.70/25.72 | ~ (is_a_theorem @
% 150.70/25.72 (equivalent @ X1 @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a))))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl29, zip_derived_cl3])).
% 150.70/25.72 thf(zip_derived_cl167, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X1)
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)) @
% 150.70/25.72 (equivalent @ X0 @ X1))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl104])).
% 150.70/25.72 thf(zip_derived_cl300, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X1)
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)) @
% 150.70/25.72 X0))
% 150.70/25.72 | ~ (is_a_theorem @ X1))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl167])).
% 150.70/25.72 thf(zip_derived_cl303, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)) @
% 150.70/25.72 X0))
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @ X1))),
% 150.70/25.72 inference('simplify', [status(thm)], [zip_derived_cl300])).
% 150.70/25.72 thf(zip_derived_cl329, plain,
% 150.70/25.72 (![X0 : $i]:
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)) @
% 150.70/25.72 X0))
% 150.70/25.72 | ~ (is_a_theorem @ X0))),
% 150.70/25.72 inference('condensation', [status(thm)], [zip_derived_cl303])).
% 150.70/25.72 thf(zip_derived_cl331, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 ~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @ X1 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)))) @
% 150.70/25.72 (equivalent @ X1 @ X0)))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl329])).
% 150.70/25.72 thf(zip_derived_cl11, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X2)
% 150.70/25.72 | ~ (is_a_theorem @ X0)
% 150.70/25.72 | ~ (is_a_theorem @ (equivalent @ X1 @ X0))
% 150.70/25.72 | (is_a_theorem @ (equivalent @ X2 @ X1)))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl5])).
% 150.70/25.72 thf(zip_derived_cl352, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @ X1 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)))))
% 150.70/25.72 | ~ (is_a_theorem @ X2)
% 150.70/25.72 | ~ (is_a_theorem @ (equivalent @ (equivalent @ X1 @ X0) @ X2)))),
% 150.70/25.72 inference('s_sup+', [status(thm)], [zip_derived_cl331, zip_derived_cl11])).
% 150.70/25.72 thf(zip_derived_cl411, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X2)
% 150.70/25.72 | ~ (is_a_theorem @
% 150.70/25.72 (equivalent @ (equivalent @ X1 @ X2) @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)))))
% 150.70/25.72 | ~ (is_a_theorem @ (equivalent @ X1 @ X0)))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl4, zip_derived_cl352])).
% 150.70/25.72 thf(zip_derived_cl537, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 (~ (is_a_theorem @ X1)
% 150.70/25.72 | ~ (is_a_theorem @
% 150.70/25.72 (equivalent @ (equivalent @ X0 @ X1) @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a))))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl513, zip_derived_cl411])).
% 150.70/25.72 thf(zip_derived_cl816, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.72 ~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.72 (equivalent @ X3 @ X2)) @
% 150.70/25.72 (equivalent @ X1 @ X0)) @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @ b @ a)))))),
% 150.70/25.72 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl537])).
% 150.70/25.72 thf(zip_derived_cl43489, plain,
% 150.70/25.72 (![X0 : $i]:
% 150.70/25.72 ~ (is_a_theorem @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @ (equivalent @ b @ a) @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @ X0))))),
% 150.70/25.72 inference('s_sup-', [status(thm)],
% 150.70/25.72 [zip_derived_cl40619, zip_derived_cl816])).
% 150.70/25.72 thf(zip_derived_cl31994, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 150.70/25.72 ( (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ X2 @ (equivalent @ X3 @ X1)) @
% 150.70/25.72 (equivalent @ X3 @ X2)) @
% 150.70/25.72 (equivalent @ X1 @ X0)))
% 150.70/25.72 | ~ (is_a_theorem @ X0))),
% 150.70/25.72 inference('condensation', [status(thm)], [zip_derived_cl672])).
% 150.70/25.72 thf(zip_derived_cl43591, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i]:
% 150.70/25.72 ~ (is_a_theorem @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @ c) @
% 150.70/25.72 (equivalent @
% 150.70/25.72 (equivalent @ X0 @ (equivalent @ X1 @ (equivalent @ b @ a))) @
% 150.70/25.72 (equivalent @ X1 @ X0))))),
% 150.70/25.72 inference('s_sup+', [status(thm)],
% 150.70/25.72 [zip_derived_cl43489, zip_derived_cl31994])).
% 150.70/25.72 thf(zip_derived_cl47164, plain,
% 150.70/25.72 (~ (is_a_theorem @
% 150.70/25.72 (equivalent @ c @
% 150.70/25.72 (equivalent @ (equivalent @ a @ (equivalent @ b @ c)) @
% 150.70/25.72 (equivalent @ b @ a))))),
% 150.70/25.72 inference('s_sup-', [status(thm)],
% 150.70/25.72 [zip_derived_cl23863, zip_derived_cl43591])).
% 150.70/25.72 thf(zip_derived_cl1, plain,
% 150.70/25.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 150.70/25.72 (is_a_theorem @
% 150.70/25.72 (equivalent @ X0 @
% 150.70/25.72 (equivalent @ (equivalent @ X1 @ (equivalent @ X2 @ X0)) @
% 150.70/25.72 (equivalent @ X2 @ X1))))),
% 150.70/25.72 inference('cnf', [status(esa)], [xgk])).
% 150.70/25.72 thf(zip_derived_cl47174, plain, ($false),
% 150.70/25.72 inference('demod', [status(thm)], [zip_derived_cl47164, zip_derived_cl1])).
% 150.70/25.72
% 150.70/25.72 % SZS output end Refutation
% 150.70/25.72
% 150.70/25.72
% 150.70/25.72 % Terminating...
% 150.70/25.77 % Runner terminated.
% 150.70/25.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------